• Journal of the Korea Society of Computer and Information
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• v.17 no.1
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• pp.161-169
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• 2012

In general, Euclidean minimum spanning tree is a tree connecting input nodes with minimum connecting cost. But the tree may not be optimal when applied to real world problems of three dimension. In this paper, three dimension Euclidean minimum spanning tree is proposed, connecting all input nodes of 3-dimensional space with minimum cost. In experiments for 30,000 input nodes with 100% space ratio, the tree produced by the proposed method can reduce 90.0% connection cost tree, compared with the tree by two dimension Prim's minimum spanning tree. In two dimension plane, the proposed tree increases 251.2% connecting cost, which is pointless in 3-dimensional real world. Therefore, the proposed method can work well for many connecting problems in real world space of three dimensions.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1007-1021
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• 2004

In this paper, we study rotation surfaces in the Minkowski 3-dimensional space with pointwise 1-type Gauss map and obtain by the use of the concept of pointwise finite type Gauss map, a characterization theorem concerning rotation surfaces and constancy of the mean curvature of certain open subsets on these surfaces.

• The Korean Journal of Community Living Science
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• v.22 no.1
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• pp.95-102
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• 2011

The purpose of this study was to examine the development of detailed description for drawing houses according to the shapes of lines, and dimensions of space from 4 to 5 years-old children. Participants were 76 children from a daycare center in Busan, Korea. Each child was asked to draw 4 different houses according to the shapes of lines and dimensions of space, such as: straight lines and 2-dimensional pictures straight lines and 3-dimensional Models, curved lines and 2-dimensional pictures and curved lines and 3-dimensional models. The children's drawings were scored based on a "detailed description rating table" which consisted of 10 items. Summarizing the overall results, first, 5 year-olds scored significantly higher than 4 year-olds in the detailed description of 4 different house models. Second, the houses with straight lines scored significantly higher than those with curved lines in the detailed description. Third, there were no significant differences between 2-dimensional houses and those of 3-dimensional models in the detailed description. These results suggest that the detailed description of young children's drawing is developed as children grow older, and drawing with straight lines are earlier developed than curved lined drawings.

• Geophysics and Geophysical Exploration
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• v.5 no.2
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• pp.71-77
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• 2002

We developed a modeling and visualization software that can analyze 3-dimensional seismic data. The software divides 3 dimensional space into a series of vertical and horizontal polygons, and allows the various seismic attributes and other spatial information to be stored on these polygons. The program can pick a particular pattern in semi-automatic mode, and store the pattern in the spatial DB. The pattern can be modeled and visualized in 3 dimensional space.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.519-529
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• 2002

In this paper. We Study (n + 1)-dimensional Contact CR-submanifolds of (n - 1) contact CR-dimension immersed in a Sasakian space form M$\^$2m+1/(c) (2m=n+p, p>0), and especially determine such submanifolds under additional condition concerning with shape operator.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.757-774
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• 2024

In three dimensional Euclidean space we consider kinematical invariants of the surface which is generated by the motion of a planar curve, especially, the surface which is foliated by circles. At first we characterize the properties of single parameter plane with the theories of unit spherical curve in three dimensional Euclidean space. Then using these results we give the invariants and differential invariants, kinematical properties and some special examples of the surface foliated by circles. The methods established here can be used to the other kinds of the surface in three dimensional Euclidean space.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.457-467
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• 2011

In this paper, we establish some comparison theorems about volumes of tubes in metric spaces with nonpositive curvature. First we compare the Hausdorff measure of tube about a metric ball contained in an (n-1)-dimensional totally geodesic subspace of an n-dimensional locally compact, geodesically complete Hadamard space with Lebesgue measure of its corresponding tube in Euclidean space ${\mathbb{R}}^n$, and then develop the result to the case of an m-dimensional totally geodesic subspace for 1 < m < n with an additional condition. Also, we estimate the Hausdorff measure of the tube about a shortest curve in a metric space of curvature bounded above and below.

• Journal of information and communication convergence engineering
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• v.10 no.4
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• pp.349-358
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• 2012

Over a wireless sensor network (WSN), accurate localization of sensor nodes is an important factor in enhancing the association between location information and sensory data. There are many research works on the development of a localization algorithm over three-dimensional (3D) space. Recently, the complexity-reduced 3D trilateration localization approach (COLA), simplifying the 3D computational overhead to 2D trilateration, was proposed. The method provides proper accuracy of location, but it has a high computational cost. Considering practical applications over resource constrained devices, it is necessary to strike a balance between accuracy and computational cost. In this paper, we present a novel 3D localization method based on the received signal strength indicator (RSSI) values of four anchor nodes, which are deployed in the initial setup process. This method provides accurate location estimation results with a reduced computational cost and a smaller number of anchor nodes.

• 전자공학회논문지 IE
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• v.47 no.4
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• pp.53-58
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• 2010

In this paper we propose symbol decision method reflecting the color non-uniformity in 3-dimensional color space. By comparing with 2-dimensional color space decision method, we show the superiority of BER performance of the proposed method. Proposed method may reflect the non-uniformity since the symbol decision boundary in color space is transformed from 3D RGB space, and one dimension corresponding to Y value is added. Therefore, we can obtain the better BER performance by using the symbol decision method in 3D color space. In this paper, through numerical simulation, show the superior BER performance of 3D color space symbol decision method compared with 2D color space symbol decision method under AWGN and common mode noise channel.